Prove this

Given point A,B,C, create three ellipses by using two of the points as focii, and the last one as a point on the ellipse, ellipse A, B and C. Ellipse A and B intersects at point I, H. Ellipse B and C intersects at point E, F. Ellipse C and A intersects at point D, G. Connect IH, EF, CA. Prove that IH, EF, CA intersects at a single point.

I’m not very good at English, so focus at the graph more.

#Geometry

Easy Math Editor

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Comments

I once did the same thing but do not have a proof for this. Also there is a generalization: if three ellipses with focii (A,B);(B,C);(C,A) does intersect at six points(any two of them intersect at two points), then the three lines are concurrent.

X X - 11 months, 3 weeks ago

Ahh, found it! [http://www.jcgeometry.org/Articles/Volume1/JCG2012V1pp1-5.pdf]

X X - 11 months, 3 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$